Determine the thermal pressure coefficient of dry air at constant volume (α_v) across temperatures from 0.0 °C to 80.0 °C using a constant-volume air thermometer (Jolly bulb) with a mercury manometer, verify the linear pressure-temperature relation P = P_0(1 + α_v t), and extrapolate to calculate the absolute zero of temperature. Explore a virtual apparatus, collect readings and analyse a graph.
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Readings are generated by an ideal model. The diagram is schematic and is not to scale.
The teaching model assumes dry air behaves as a classical ideal gas with negligible intermolecular van der Waals forces and zero dead-space volume in the capillary stem. In a physical laboratory, small corrections must be applied for capillary dead space (~0.6% unheated volume), cubical thermal expansion of the borosilicate glass envelope (γ ≈ 9.9 × 10⁻⁶ K⁻¹), and real-gas virial departures. The linear relationship P = P_0(1 + α_v t) directly bridges classical pneumatic manometry with Kelvin’s absolute thermodynamic temperature scale. The experimental pressure coefficient α_v = 1/273.15 K⁻¹ demonstrates that gas pressure approaches zero at −273.15 °C, establishing the physical foundation for the absolute scale of temperature where T = t + 273.15.
A rigid spherical borosilicate glass bulb of nominal capacity 100.00 cm³ terminating in a narrow capillary stem, enclosing a fixed dry air charge and designed for total immersion in the variable-temperature bath.
Two parallel glass manometer tubes: a closed limb containing a sharp downward-pointing glass fiducial index tip defining the fixed reference volume, and an open limb connected via flexible tubing to register gauge pressure Δh.
Provides fine vertical translation of the open manometer tube across a 600 mm range, allowing the operator to adjust the mercury column height precisely until the closed-tube meniscus touches the index pointer.
A transparent cylindrical jacket surrounding the bulb, equipped with an electric heating element and a motorized propeller stirrer to ensure homogeneous temperature distribution throughout the liquid volume without spatial gradients.
Calibrated mercury-in-glass secondary standard thermometer suspended directly adjacent to the Jolly bulb to register the bath thermal equilibrium temperature to ±0.05 °C.
Measures the prevailing ambient atmospheric pressure B in millimeters of mercury (mmHg) and kilopascals (kPa), essential for converting measured manometer gauge pressure Δh into absolute gas pressure P = B + Δh.
Determine the thermal pressure coefficient of dry air at constant volume (α_v) across temperatures from 0.0 °C to 80.0 °C using a constant-volume air thermometer (Jolly bulb) with a mercury manometer, verify the linear pressure-temperature relation P = P_0(1 + α_v t), and extrapolate to calculate the absolute zero of temperature. Suggested independent settings: 0.0, 20.0, 40.0, 60.0, 80.0 °C.
Read the laboratory Fortin mercurial barometer to 0.1 mmHg, applying brass scale and temperature reductions to determine the true ambient atmospheric pressure B (nominal baseline B = 760.0 mmHg = 101.325 kPa). Inspect the Jolly bulb capillary and manometer tubes to verify that the mercury surfaces are clean, free of oxidation films, and that no air bubbles reside in the flexible connecting hose.
Because the open limb of the manometer is exposed to the room, the absolute pressure of the confined gas is the sum of atmospheric pressure and the differential mercury head (P = B + Δh). An accurate barometric reading is essential for absolute pressure calculations.
Fill the bath vessel surrounding the Jolly bulb with finely crushed pure melting ice and distilled water. Agitate the slurry thoroughly for at least five minutes until the immersion thermometer stabilizes at 0.00 °C. Adjust the movable open manometer tube until the apex of the convex mercury meniscus in the closed capillary just touches the sharp tip of the fiducial index pointer. Sighting with an optical magnifier, confirm zero differential head between the two tubes (Δh = 0) at 0 °C, establishing the baseline absolute pressure P_0 = 101.325 kPa.
Bringing the mercury meniscus precisely to the fiducial pointer fixes the enclosed gas volume to the invariant reference value V_0, while the ice bath provides the fundamental thermodynamic reference baseline for computing the thermal pressure coefficient α_v.
Drain the ice water and fill the jacket with tap water. Energize the electric heater to raise the bath temperature progressively in 20.0 °C increments (20.0 °C, 40.0 °C, 60.0 °C, 80.0 °C). Run the motorized stirrer continuously at moderate speed to circulate the water around the spherical bulb and prevent thermal stratification.
Continuous mechanical agitation prevents convective hot spots from developing near the heating element, ensuring that the enclosed air reaches the exact temperature registered by the immersion thermometer.
As the gas temperature rises, the increased internal thermal pressure tends to depress the mercury in the closed capillary. Use the fine rack-and-pinion control to raise the open leveling tube until the mercury meniscus in the closed limb is restored exactly to touch the fiducial index pointer tip. Confirm that no gap and no meniscus deformation exists at the contact point.
This restoration step enforces the fundamental condition of Charles’ law: the gas volume is held strictly constant (dV = 0) so that the entire thermal energy input manifests solely as an increase in thermodynamic pressure.
Once thermal equilibrium is established (constant temperature for at least 3 minutes), record the bath temperature t to the nearest 0.1 °C. Read the heights of the mercury columns in the closed tube (h_closed) and open tube (h_open) on the mirror-backed millimeter scale. Calculate the gauge head Δh = h_open − h_closed and compute the absolute pressure P = B + Δh in kilopascals (kPa).
Mirror-backed scale readings eliminate optical parallax error. Recording paired values of t and P under verified thermal equilibrium ensures high fidelity in the subsequent linear regression analysis.
De-energize the heater and allow the bath to cool slowly, recording repeat pressure readings at the same temperature stations with falling temperatures to check for thermal hysteresis or gas leakage. Plot the equilibrium absolute pressure P against Celsius temperature t, compute the best-fit slope m and intercept b, and extrapolate the line to P = 0 to calculate the absolute zero of temperature T_0 = −b / m.
Verifying identical readings during cooling confirms that no gas leaked past the mercury seal and that the glass bulb underwent elastic, reversible thermal cycling.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Bath temperature t (°C) | Absolute pressure P (kPa) | Temperature t (°C) | Absolute pressure P (kPa) | Remove |
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